תאריך:
ה', 19/06/202514:30-15:30
מיקום:
Manchester, Hall 2
Title: Product mixing in groups
Absract:
Let A, B, C be subsets of the special unitary group SU(n) of Haar measure ≥ e^{−n^1/3}. Then ABC = SU(n). In fact, the product abc of random elements a ∼ A, b ∼ B, c ∼ C is equidistributed in SU(n).
This makes progress on a question that was posed independently by Gowers studying nonabelian variants of questions from additive combinatorics and settles a conjecture of physicists studying quantum communication complexity.
To prove our results we introduce a tool known as ‘hypercontractivity’ to the study of high rank compact Lie groups. We then show that it synergies with their representation theory to obtain our result.
Based on a joint work with Ellis, Kindler, and Minzer.
Absract:
Let A, B, C be subsets of the special unitary group SU(n) of Haar measure ≥ e^{−n^1/3}. Then ABC = SU(n). In fact, the product abc of random elements a ∼ A, b ∼ B, c ∼ C is equidistributed in SU(n).
This makes progress on a question that was posed independently by Gowers studying nonabelian variants of questions from additive combinatorics and settles a conjecture of physicists studying quantum communication complexity.
To prove our results we introduce a tool known as ‘hypercontractivity’ to the study of high rank compact Lie groups. We then show that it synergies with their representation theory to obtain our result.
Based on a joint work with Ellis, Kindler, and Minzer.